Results 1 to 4 of 4

Math Help - Epsilon delta definition of limit

  1. #1
    Member roshanhero's Avatar
    Joined
    Aug 2008
    Posts
    180

    Epsilon delta definition of limit

    How to prove that \lim_{x\to2}{x^2}=4 by using the formal definition of limit?
    I tried to solve it, but the problem was to find delta that depends on epsilon.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    Consider:

    \left |{x^2-4}\right |< \epsilon \Leftrightarrow \left |{x-2}\right |\left |{x+2}\right |< \epsilon

    For choosing \delta take into account that |x+2| is (for example) bounded on [1,3].

    Regards.

    Fernando Revilla
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member roshanhero's Avatar
    Joined
    Aug 2008
    Posts
    180
    I am sorry, but I still couldnot get it.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor FernandoRevilla's Avatar
    Joined
    Nov 2010
    From
    Madrid, Spain
    Posts
    2,162
    Thanks
    45
    On (1,3) we have |x+2|<5,

    then, on (1,3)

    |x^2-4|=|x-2||x+2|<5|x-2|<\epsilon \Leftrightarrow |x-2|<\epsilon/5

    Now, choose

    \delta=\min\{1,\epsilon/5\}

    Regards.

    http://www.fernandorevilla.es/
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Epsilon delta definition of limit.
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 20th 2011, 06:20 PM
  2. Replies: 3
    Last Post: February 21st 2011, 08:11 AM
  3. [SOLVED] Epsilon Delta (limit definition)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 21st 2010, 08:39 AM
  4. Prove limit with epsilon-delta definition.
    Posted in the Calculus Forum
    Replies: 3
    Last Post: August 30th 2009, 05:19 PM
  5. Epsilon-Delta Limit Definition
    Posted in the Calculus Forum
    Replies: 3
    Last Post: March 25th 2009, 02:20 PM

Search Tags


/mathhelpforum @mathhelpforum